8,575 research outputs found
Probing dark energy with future surveys
I review the observational prospects to constrain the equation of state parameter of dark energy and I discuss the potential of future imaging and redshift surveys. Bayesian model selection is used to address the question of the level of accuracy on the equation of state parameter that is required before explanations alternative to a cosmological constant become very implausible. I discuss results in the prediction space of dark energy models. If no significant departure from w=-1 is detected, a precision on w of order 1% will translate into strong evidence against fluid-like dark energy, while decisive evidence will require a precision of order 10^-3
The cosmological constant and the paradigm of adiabaticity
We discuss the value of the cosmological constant as recovered from CMB and
LSS data and the robustness of the results when general isocurvature initial
conditions are allowed for, as opposed to purely adiabatic perturbations. The
Bayesian and frequentist statistical approaches are compared. It is shown that
pre-WMAP CMB and LSS data tend to be incompatible with a non-zero cosmological
constant, regardless of the type of initial conditions and of the statistical
approach. The non-adiabatic contribution is constrained to be < 40% (2sigma
c.l.).Comment: 9 pages, 5 figures, to appear in New Astronomy Reviews, Proceedings
of the 2nd CMBNET Meeting, 20-21 February 2003, Oxford, U
Applications of Bayesian model selection to cosmological parameters
Bayesian model selection is a tool to decide whether the introduction of a
new parameter is warranted by data. I argue that the usual sampling statistic
significance tests for a null hypothesis can be misleading, since they do not
take into account the information gained through the data, when updating the
prior distribution to the posterior. On the contrary, Bayesian model selection
offers a quantitative implementation of Occam's razor.
I introduce the Savage-Dickey density ratio, a computationally quick method
to determine the Bayes factor of two nested models and hence perform model
selection. As an illustration, I consider three key parameters for our
understanding of the cosmological concordance model. By using WMAP 3-year data
complemented by other cosmological measurements, I show that a non-scale
invariant spectral index of perturbations is favoured for any sensible choice
of prior. It is also found that a flat Universe is favoured with odds of 29:1
over non--flat models, and that there is strong evidence against a CDM
isocurvature component to the initial conditions which is totally
(anti)correlated with the adiabatic mode (odds of about 2000:1), but that this
is strongly dependent on the prior adopted.
These results are contrasted with the analysis of WMAP 1-year data, which
were not informative enough to allow a conclusion as to the status of the
spectral index. In a companion paper, a new technique to forecast the Bayes
factor of a future observation is presented.Comment: v2 to v3: minor changes, matches accepted version by MNRAS. v1 to v2:
major revision. New results using WMAP 3-yr data, scale-invariant spectrum
now disfavoured with moderate evidence. New benchmark test for the accuracy
of the method. Bayes factor forecast methodology (PPOD, formerly called ExPO)
expanded and now presented in a companion paper (astro-ph/0703063
Bayesian Calibrated Significance Levels Applied to the Spectral Tilt and Hemispherical Asymmetry
Bayesian model selection provides a formal method of determining the level of
support for new parameters in a model. However, if there is not a specific
enough underlying physical motivation for the new parameters it can be hard to
assign them meaningful priors, an essential ingredient of Bayesian model
selection. Here we look at methods maximizing the prior so as to work out what
is the maximum support the data could give for the new parameters. If the
maximum support is not high enough then one can confidently conclude that the
new parameters are unnecessary without needing to worry that some other prior
may make them significant. We discuss a computationally efficient means of
doing this which involves mapping p-values onto upper bounds of the Bayes
factor (or odds) for the new parameters. A p-value of 0.05 ()
corresponds to odds less than or equal to 5:2 which is below the `weak' support
at best threshold. A p-value of 0.0003 () corresponds to odds of
less than or equal to 150:1 which is the `strong' support at best threshold.
Applying this method we find that the odds on the scalar spectral index being
different from one are 49:1 at best. We also find that the odds that there is
primordial hemispherical asymmetry in the cosmic microwave background are 9:1
at best.Comment: 5 pages. V2: clarifying comments added in response to referee report.
Matches version to appear in MNRA
Testing the paradigm of adiabaticity
We introduce the concepts of adiabatic (curvature) and isocurvature (entropy)
cosmological perturbations and present their relevance for parameter estimation
from cosmic microwave background anisotropies data. We emphasize that, while
present-day data are in excellent agreement with pure adiabaticity, subdominant
isocurvature contributions cannot be ruled out. We discuss model independent
constraints on the isocurvature contribution. Finally, we argue that the Planck
satellite will be able to do precision cosmology even if the assumption of
adiabaticity is relaxed.Comment: Proceedings of the 10th Marcel Grossmann Meeting, Rio de Janeiro,
July 2003, 5 pages, 2 figure
Statistical Challenges of Global SUSY Fits
We present recent results aiming at assessing the coverage properties of Bayesian and frequentist inference methods, as applied to the reconstruction of supersymmetric parameters from simulated LHC data. We discuss the statistical challenges of the reconstruction procedure, and highlight the algorithmic difficulties of obtaining accurate profile likelihood estimates
Constraining the helium abundance with CMB data
We consider for the first time the ability of present-day cosmic microwave background (CMB) anisotropies data to determine the primordial helium mass fraction, Y_p. We find that CMB data alone gives the confidence interval 0.160 < Y_p < 0.501 (at 68% c.l.). We analyse the impact on the baryon abundance as measured by CMB and discuss the implications for big bang nucleosynthesis. We identify and discuss correlations between the helium mass fraction and both the redshift of reionization and the spectral index. We forecast the precision of future CMB observations, and find that Planck alone will measure Y_p with error-bars of 5%. We point out that the uncertainty in the determination of the helium fraction will have to be taken into account in order to correctly estimate the baryon density from Planck-quality CMB data
Why anthropic reasoning cannot predict Lambda
We revisit anthropic arguments purporting to explain the measured value of
the cosmological constant. We argue that different ways of assigning
probabilities to candidate universes lead to totally different anthropic
predictions. As an explicit example, we show that weighting different universes
by the total number of possible observations leads to an extremely small
probability for observing a value of Lambda equal to or greater than what we
now measure. We conclude that anthropic reasoning within the framework of
probability as frequency is ill-defined and that in the absence of a
fundamental motivation for selecting one weighting scheme over another the
anthropic principle cannot be used to explain the value of Lambda, nor, likely,
any other physical parameters.Comment: 4 pages, 1 figure. Discussion slighlty expanded, refs added,
conclusions unchanged. Matches published versio
The Virtues of Frugality - Why cosmological observers should release their data slowly
Cosmologists will soon be in a unique position. Observational noise will
gradually be replaced by cosmic variance as the dominant source of uncertainty
in an increasing number of observations. We reflect on the ramifications for
the discovery and verification of new models. If there are features in the full
data set that call for a new model, there will be no subsequent observations to
test that model's predictions. We give specific examples of the problem by
discussing the pitfalls of model discovery by prior adjustment in the context
of dark energy models and inflationary theories. We show how the gradual
release of data can mitigate this difficulty, allowing anomalies to be
identified, and new models to be proposed and tested. We advocate that
observers plan for the frugal release of data from future cosmic variance
limited observations.Comment: 5 pages, expanded discussion of Lambda and of blind anlysis, added
refs. Matches version to appear in MNRAS Letter
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